$A$ cylindrical vessel of cross-sectional area $1000 \ cm^2$ is fitted with a frictionless piston of mass $10 \ kg$ and filled with water completely. $A$ small hole of cross-sectional area $10 \ mm^2$ is opened at a point $50 \ cm$ deep from the lower surface of the piston. The velocity of efflux from the hole will be ........... $m/s$.

$A$ large vessel with a small hole at the bottom is filled with water and kerosene, with kerosene floating on water. The length of the water column is $20 \,cm$ and that of the kerosene is $25 \,cm$. The velocity with which water flows out of the hole is (density of kerosene $= 0.8 \,g/cm^3$, density of water $= 1.0 \,g/cm^3$, neglect viscous force). (in $\,m/s$)

In a cylindrical water tank,there are two small holes $A$ and $B$ on the wall. Hole $A$ is at a depth of $h_1$ from the water surface,and hole $B$ is at a height of $h_2$ from the bottom of the tank. The total height of the water surface from the bottom of the tank is $H$. Water coming out from both holes strikes the ground at the same point $S$. Find the ratio of $h_1$ and $h_2$.

$A$ cylindrical vessel open at the top is $20 \ cm$ high and $10 \ cm$ in diameter. $A$ circular hole whose cross-sectional area is $1 \ cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of $100 \ cm^3 s^{-1}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g = 1000 \ cm s^{-2}$)

Two large,identical water tanks,$1$ and $2$,kept on the top of a building of height $H$,are filled with water up to height $h$ in each tank. Both the tanks contain an identical hole of small radius on their sides,close to their bottom. $A$ pipe of the same internal radius as that of the hole is connected to tank $2$,and the pipe ends at the ground level. When the water flows out of tanks $1$ and $2$ through the holes,the times taken to empty the tanks are $t_1$ and $t_2$,respectively. If $H = (16/9) h$,then the ratio $t_1 / t_2$ is:

$A$ rectangular tank is placed on a horizontal ground and is filled with water to a height $H$ above the base. $A$ small hole is made on one vertical side at a depth $D$ below the level of the water in the tank. The distance $x$ from the bottom of the tank at which the water jet from the tank will hit the ground is